Finite Group Databasebeta

← #16857747

Subgroups — #16857747

Order 3968.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521769C211yesmaximal, characteristic, complemented
2#14521408C211yesmaximal, characteristic, complemented
3#14521387C211yesmaximal, characteristic, complemented
4#14521370C211yesmaximal, characteristic, complemented
5#14521339C211yesmaximal, characteristic, complemented
6#14521305C211yesmaximal, characteristic, complemented
7#14521276C211yesmaximal, characteristic, complemented
8#14521268C211yesmaximal, characteristic, complemented
9#14521211C211yesmaximal, characteristic, complemented
10#14521200C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521054C211yesmaximal, characteristic, complemented
14#14521045C211yesmaximal, characteristic, complemented
15C31×#546C211yesmaximal, characteristic
16C2×#41×C31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C31×#124C2211yescharacteristic
19C31×#123—21no—
20C31×C22⋊Q8C2211yescharacteristic
21C31×#121—21no—
22C31×#121C2211yescharacteristic
23C31×#120—21no—
24C4×D4×C31C2211yescharacteristic
25C4×D4×C31C2211yescharacteristic
26C2×C22⋊C4×C31—21no—
27C2×#92482C2211yescharacteristic, complemented
28#11758513—21no—
29C2×#92480C2211yescharacteristic
30C2×#92480C2211yescharacteristic
31#11758503C2211yescharacteristic
32#11758503C2211yescharacteristic, complemented
33#11758501C2211yescharacteristic
34#11758501C2211yescharacteristic, complemented
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic, complemented
37#11758464—21no—
38#11758456—21no—
39#11758456—21no—
40#11758446C2211yescharacteristic, complemented
41C4×Dic62C2211yescharacteristic, complemented
42#11758423C2211yescharacteristic, complemented
43#11758423C2211yescharacteristic, complemented
44#11758423C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758396C2211yescharacteristic, complemented
55#11758396C2211yescharacteristic, complemented
56#11758395C2211yescharacteristic, complemented
57C4⋊(C31⋊C8)C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C24×C31—21no—
60#41×C31—22no—
61#41×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—22no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—41no—
68C2×D4×C31D411yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C2×D4×C31C2311yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31C2311yescharacteristic
74C22×C4×C31C2311yescharacteristic
75C2×Dic62—21no—
76C2×Dic62C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31D411yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C22⋊C4×C31D411yescharacteristic
86C22⋊C4×C31D411yescharacteristic
87C42×C31C2311yescharacteristic
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92#92482—41no—
93#92480—22no—
94#92480—41no—
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105#92474—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—42no—
114C23×C31—42no—
115C23×C31—81no—
116C23×C31C2×D411yescharacteristic
117C23×C31C2×D411yescharacteristic
118Q8×C31—21no—
119Q8×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—21no—
123D4×C31—41no—
124D4×C31—42no—
125D4×C31—42no—
126D4×C31—81no—
127D4×C31#4112yes—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—42no—
135C2×C4×C31—81no—
136C2×C4×C31C2×D411yescharacteristic
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2411yescharacteristic
141C2×Dic31—21no—
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—21no—
145Dic62—21no—
146Dic62—21no—
147Dic62—42no—
148C31⋊C8—21no—
149C31⋊C8—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3311—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—22no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—84no—
166C22×C31C22×D411yescharacteristic
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31C2×#4111yescharacteristic
174C4×C31H(5,𝔽2)11yescharacteristic
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178Dic31—41no—
179#556—311no—
180#546D3111yescharacteristic
181#489—311no—
182#485—311no—
183#482—311no—
184#476—311no—
185#470—311no—
186#465—311no—
187#464—311no—
188#452—311no—
189#450—311no—
190#440—311no—
191#435—311no—
192#418—311no—
193#416—311no—
194C2×C31—41no—
195C2×C31—41no—
196C2×C31—42no—
197C2×C31—81no—
198C2×C31#54611yescharacteristic
199C2×C31#57511yescharacteristic
200C2×C31#57711yescharacteristic
201C2×#41C2×D3111yescharacteristic
202C22×D4C2×D3111yescharacteristic
203C2×Q16—311no—
204C2×SD16—311no—
205C2×SD16—311no—
206C2×M16—311no—
207C22×C8—311no—
208C4⋊Q8—311no—
209#126—621no—
210#126—621no—
211#124—621no—
212#124C2×D3111yescharacteristic
213#123—21no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8C2×D3111yescharacteristic
217#121—21no—
218#121C2×D3111yescharacteristic
219#120—21no—
220C4×Q8—311no—
221C4×Q8—621no—
222C4×D4C2×D3111yescharacteristic
223C4×D4C2×D3111yescharacteristic
224#117—311no—
225#117—311no—
226C2×C22⋊C4—21no—
227#107—311no—
228#106—311no—
229#106—311no—
230C4⋊C8—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103—311no—
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241C22⋊C8—311no—
242C22⋊C8—311no—
243#97—311no—
244C31#331111yescharacteristic, complemented, Sylow
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—311no—
249C2×Q8—621no—
250C2×Q8C22×D3111yescharacteristic
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4C22⋊D3111yescharacteristic
257C2×D4C22×D3111yescharacteristic
258C2×D4C22×D3111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C22×D3111yescharacteristic
262C22×C4C22×D3111yescharacteristic
263Q16—1241no—
264SD16—622no—
265SD16—1241no—
266M16—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—311no—
271C2×C8—1241no—
272C4⋊C4—21no—
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4C22⋊D3111yescharacteristic
281C4⋊C4C22×D3111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4C22⋊D3111yescharacteristic
292C22⋊C4C22⋊D3111yescharacteristic
293C42—621no—
294C42—621no—
295C42—621no—
296C42C22×D3111yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D3111yescharacteristic
303C23C2×C22⋊D3111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—621no—
307Q8—621no—
308Q8—1242no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—81no—
316D4#9249712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4C2×C22⋊D3111yescharacteristic
330C2×C4C2×C22⋊D3111yescharacteristic
331C2×C4C2×C22⋊D3111yescharacteristic
332C2×C4C2×C22⋊D3111yescharacteristic
333C2×C4C23×D3111yescharacteristic
334C8—621no—
335C8—621no—
336C8—621no—
337C8—621no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D3111yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—1241no—
359C4—1241no—
360C4—1241no—
361C4—1241no—
362C4C2×#9249711yescharacteristic
363C4#1175856111yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1452169311yescharacteristic
369C2#1452184711yescharacteristic
370C2#1452186011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#546C2
socleC22×C31C22×D4
hypercenter#546D31
hypocenterC31#3311
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14521769C2semidirect
2. #14521408C2semidirect
3. #14521387C2semidirect
4. #14521370C2semidirect
5. #14521339C2semidirect
6. #14521305C2semidirect
7. #14521276C2semidirect
8. #14521268C2semidirect
9. #14521211C2semidirect
10. #14521200C2semidirect
11. #14521149C2semidirect
12. #14521121C2semidirect
13. #14521054C2semidirect
14. #14521045C2semidirect
27. C2×#92482C22semidirect
32. #11758503C22semidirect
34. #11758501C22semidirect
36. C22×C31⋊C8C22semidirect
40. #11758446C22semidirect
41. C4×Dic62C22semidirect
42. #11758423C22semidirect
43. #11758423C22semidirect
44. #11758423C22semidirect
52. C22⋊(C31⋊C8)C22semidirect
53. #11758398C22semidirect
54. #11758396C22semidirect
55. #11758396C22semidirect
56. #11758395C22semidirect
57. C4⋊(C31⋊C8)C22semidirect
58. #11758391C22semidirect
244. C31#3311semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145217692
#145214082
#145213872
#145213702
#145213392
#145213052
#145212762
#145212682
#145212112
#145212002
#145211492
#145211212
#145210542
#145210452
C31×#5462
#331131